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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [2, 2, 4, 30], 'aut_gens': [[1, 2, 24], [13, 2, 24], [1, 10, 24], [1, 10, 72], [17, 62, 24]], 'aut_group': '480.1197', 'aut_hash': 1197, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 480, 'aut_permdeg': 12, 'aut_perms': [90720, 3669840, 3719538, 79874711], 'aut_phi_ratio': 15.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 2, 1, 1], [4, 6, 1, 1], [4, 10, 1, 1], [4, 30, 1, 1], [5, 2, 2, 1], [6, 2, 1, 1], [10, 2, 2, 1], [12, 10, 2, 1], [15, 4, 2, 1], [20, 6, 4, 1], [30, 4, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_6\\times F_5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '120.36', 'autcentquo_hash': 36, 'autcentquo_nilpotent': False, 'autcentquo_order': 120, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 2, 1], [4, 6, 1], [4, 10, 1], [4, 30, 1], [5, 2, 2], [6, 2, 1], [10, 2, 2], [12, 10, 2], [15, 4, 2], [20, 6, 4], [30, 4, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '60.8', 'commutator_count': 1, 'commutator_label': '30.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 14, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 2, 1, 1], [4, 6, 1, 1], [4, 10, 1, 1], [4, 30, 1, 1], [5, 2, 2, 1], [6, 2, 1, 1], [10, 2, 2, 1], [12, 10, 2, 1], [15, 4, 2, 1], [20, 6, 4, 1], [30, 4, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 60, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, -1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '60.8', 'hash': 14, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 6, 5], 'inner_gens': [[1, 22, 24], [5, 2, 96], [1, 50, 24]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 60, 'inner_split': True, 'inner_tex': 'S_3\\times D_5', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 8, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 4], [2, 13], [4, 4]], 'label': '120.14', 'linC_count': 26, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 7, 'linQ_dim': 10, 'linQ_dim_count': 4, 'linR_count': 16, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C15:Q8', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 13, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 21, 'number_divisions': 13, 'number_normal_subgroups': 14, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 24, 'number_subgroups': 76, 'old_label': None, 'order': 120, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 46], [5, 4], [6, 2], [10, 4], [12, 20], [15, 8], [20, 24], [30, 8]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 10, 24], [1, 2, 48]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 3], [8, 3]], 'representations': {'PC': {'code': 152412364976812055559, 'gens': [1, 2, 5], 'pres': [5, -2, -2, -2, -3, -5, 60, 221, 26, 302, 42, 323, 1209]}, 'GLZN': {'d': 2, 'p': 30, 'gens': [302101, 40966, 252261, 297011, 27181]}, 'Perm': {'d': 16, 'gens': [1508416318087, 2891341112400, 4302991486080, 5760, 37]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{15}:Q_8', 'transitive_degree': 120, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 108578793
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 14, 'group_order': 120, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
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id: 108578804
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 14, 'group_order': 120, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 12, 'size': 1}
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id: 108578807
{'aut_label': '3A', 'centralizer': '2.b1.a1', 'counter': 3, 'group_counter': 14, 'group_order': 120, 'label': '3A', 'order': 3, 'powers': [3, 1, 3], 'representative': 8, 'size': 2}
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id: 108578808
{'aut_label': '4A', 'centralizer': '6.b1.a1', 'counter': 4, 'group_counter': 14, 'group_order': 120, 'label': '4A', 'order': 4, 'powers': [2, 4, 4], 'representative': 1, 'size': 6}
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id: 108578809
{'aut_label': '4B', 'centralizer': '10.b1.a1', 'counter': 5, 'group_counter': 14, 'group_order': 120, 'label': '4B', 'order': 4, 'powers': [2, 5, 5], 'representative': 6, 'size': 10}
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id: 108578810
{'aut_label': '4C', 'centralizer': '30.c1.a1', 'counter': 6, 'group_counter': 14, 'group_order': 120, 'label': '4C', 'order': 4, 'powers': [2, 6, 6], 'representative': 7, 'size': 30}
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id: 108578811
{'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 7, 'group_counter': 14, 'group_order': 120, 'label': '5A1', 'order': 5, 'powers': [8, 8, 1], 'representative': 96, 'size': 2}
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id: 108578812
{'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 8, 'group_counter': 14, 'group_order': 120, 'label': '5A2', 'order': 5, 'powers': [7, 7, 1], 'representative': 72, 'size': 2}
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id: 108578813
{'aut_label': '6A', 'centralizer': '2.b1.a1', 'counter': 9, 'group_counter': 14, 'group_order': 120, 'label': '6A', 'order': 6, 'powers': [3, 2, 9], 'representative': 4, 'size': 2}
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id: 108578794
{'aut_label': '10A1', 'centralizer': '2.a1.a1', 'counter': 10, 'group_counter': 14, 'group_order': 120, 'label': '10A1', 'order': 10, 'powers': [7, 11, 2], 'representative': 60, 'size': 2}
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id: 108578795
{'aut_label': '10A1', 'centralizer': '2.a1.a1', 'counter': 11, 'group_counter': 14, 'group_order': 120, 'label': '10A3', 'order': 10, 'powers': [8, 10, 2], 'representative': 36, 'size': 2}
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id: 108578796
{'aut_label': '12A1', 'centralizer': '10.b1.a1', 'counter': 12, 'group_counter': 14, 'group_order': 120, 'label': '12A1', 'order': 12, 'powers': [9, 5, 13], 'representative': 2, 'size': 10}
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id: 108578797
{'aut_label': '12A1', 'centralizer': '10.b1.a1', 'counter': 13, 'group_counter': 14, 'group_order': 120, 'label': '12A5', 'order': 12, 'powers': [9, 5, 12], 'representative': 10, 'size': 10}
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id: 108578798
{'aut_label': '15A1', 'centralizer': '4.a1.a1', 'counter': 14, 'group_counter': 14, 'group_order': 120, 'label': '15A1', 'order': 15, 'powers': [15, 7, 3], 'representative': 56, 'size': 4}
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id: 108578799
{'aut_label': '15A1', 'centralizer': '4.a1.a1', 'counter': 15, 'group_counter': 14, 'group_order': 120, 'label': '15A2', 'order': 15, 'powers': [14, 8, 3], 'representative': 112, 'size': 4}
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id: 108578800
{'aut_label': '20A1', 'centralizer': '6.b1.a1', 'counter': 16, 'group_counter': 14, 'group_order': 120, 'label': '20A1', 'order': 20, 'powers': [10, 17, 4], 'representative': 25, 'size': 6}
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id: 108578801
{'aut_label': '20A1', 'centralizer': '6.b1.a1', 'counter': 17, 'group_counter': 14, 'group_order': 120, 'label': '20A3', 'order': 20, 'powers': [11, 19, 4], 'representative': 49, 'size': 6}
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id: 108578802
{'aut_label': '20A1', 'centralizer': '6.b1.a1', 'counter': 18, 'group_counter': 14, 'group_order': 120, 'label': '20A7', 'order': 20, 'powers': [11, 16, 4], 'representative': 73, 'size': 6}
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id: 108578803
{'aut_label': '20A1', 'centralizer': '6.b1.a1', 'counter': 19, 'group_counter': 14, 'group_order': 120, 'label': '20A9', 'order': 20, 'powers': [10, 18, 4], 'representative': 97, 'size': 6}
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id: 108578805
{'aut_label': '30A1', 'centralizer': '4.a1.a1', 'counter': 20, 'group_counter': 14, 'group_order': 120, 'label': '30A1', 'order': 30, 'powers': [14, 10, 9], 'representative': 28, 'size': 4}
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id: 108578806
{'aut_label': '30A1', 'centralizer': '4.a1.a1', 'counter': 21, 'group_counter': 14, 'group_order': 120, 'label': '30A7', 'order': 30, 'powers': [15, 11, 9], 'representative': 52, 'size': 4}
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gps_qchar • Show schema
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id: 3929422
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 3929427
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
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id: 3929428
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
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id: 3929429
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 3929430
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, -1, 0, 2, 0, 2, 2, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
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id: 3929431
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -1, 0, -2, 0, 2, 2, -1, 2, 2, 1, 1, -1, -1, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
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id: 3929432
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.2c', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, 2, 0, 0, 0, 2, 2, -2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, -2, -2], 'schur_index': 2}
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id: 3929433
{'cdim': 2, 'counter': 8, 'faithful': False, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.2d', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, -1, -1, 4, -1, -1, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 3929434
{'cdim': 2, 'counter': 9, 'faithful': False, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.2e', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 4, 4, -4, 0, 0, -1, -1, 4, -1, -1, 0, 0, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
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id: 3929423
{'cdim': 2, 'counter': 10, 'faithful': False, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.2f', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, -4, -2, 0, 0, 0, 4, 4, 2, -4, -4, 0, 0, -2, -2, 0, 0, 0, 0, 2, 2], 'schur_index': 2}
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id: 3929424
{'cdim': 2, 'counter': 11, 'faithful': False, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.2g', 'multiplicity': 4, 'nt': [40, 8], 'qdim': 8, 'qvalues': [8, -8, 8, 0, 0, 0, -2, -2, -8, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, 2, 2], 'schur_index': 2}
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id: 3929425
{'cdim': 4, 'counter': 12, 'faithful': False, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.4a', 'multiplicity': 2, 'nt': [15, 7], 'qdim': 8, 'qvalues': [8, 8, -4, 0, 0, 0, -2, -2, -4, -2, -2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
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id: 3929426
{'cdim': 4, 'counter': 13, 'faithful': True, 'group': '120.14', 'group_order': 120, 'image': None, 'label': '120.14.4b', 'multiplicity': 2, 'nt': [120, 0], 'qdim': 8, 'qvalues': [8, -8, -4, 0, 0, 0, -2, -2, 4, 2, 2, 0, 0, 1, 1, 0, 0, 0, 0, -1, -1], 'schur_index': 2}
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gps_char • Show schema
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id: 5486490
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 120, 'label': '120.14.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 5486501
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 60, 'label': '120.14.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
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id: 5486504
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 60, 'label': '120.14.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
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id: 5486505
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 60, 'label': '120.14.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 5486506
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 20, 'label': '120.14.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 5486507
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 10, 'label': '120.14.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 5486508
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 30, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.a1.a1', 'kernel_order': 15, 'label': '120.14.2c', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]]]}
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id: 5486509
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 12, 'counter': 8, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 12, 'label': '120.14.2d1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
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id: 5486510
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 12, 'counter': 9, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 12, 'label': '120.14.2d2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
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id: 5486491
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 12, 'counter': 10, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 6, 'label': '120.14.2e1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
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id: 5486492
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 12, 'counter': 11, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 6, 'label': '120.14.2e2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
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id: 5486493
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 10, 'counter': 12, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.a1.a1', 'kernel_order': 5, 'label': '120.14.2f1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
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id: 5486494
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 10, 'counter': 13, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.a1.a1', 'kernel_order': 5, 'label': '120.14.2f2', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
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id: 5486495
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 6, 'counter': 14, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '40.4', 'image_order': 40, 'indicator': -1, 'kernel': '40.a1.a1', 'kernel_order': 3, 'label': '120.14.2g1', 'nt': [40, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]]]}
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id: 5486496
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 6, 'counter': 15, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '40.4', 'image_order': 40, 'indicator': -1, 'kernel': '40.a1.a1', 'kernel_order': 3, 'label': '120.14.2g2', 'nt': [40, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-2, 0]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]]]}
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id: 5486497
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 6, 'counter': 16, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '40.4', 'image_order': 40, 'indicator': -1, 'kernel': '40.a1.a1', 'kernel_order': 3, 'label': '120.14.2g3', 'nt': [40, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-2, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]]]}
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id: 5486498
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 6, 'counter': 17, 'cyclotomic_n': 20, 'dim': 2, 'faithful': False, 'field': [5, 0, -5, 0, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '40.4', 'image_order': 40, 'indicator': -1, 'kernel': '40.a1.a1', 'kernel_order': 3, 'label': '120.14.2g4', 'nt': [40, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-2, 0]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]]]}
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id: 5486499
{'center': '60.a1.a1', 'center_index': 60, 'center_order': 2, 'counter': 18, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '60.8', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 2, 'label': '120.14.4a1', 'nt': [15, 7], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[-2, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
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id: 5486500
{'center': '60.a1.a1', 'center_index': 60, 'center_order': 2, 'counter': 19, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '60.8', 'image_order': 60, 'indicator': 1, 'kernel': '60.a1.a1', 'kernel_order': 2, 'label': '120.14.4a2', 'nt': [15, 7], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-2, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
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id: 5486502
{'center': '60.a1.a1', 'center_index': 60, 'center_order': 2, 'counter': 20, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '120.14', 'image_order': 120, 'indicator': -1, 'kernel': '120.a1.a1', 'kernel_order': 1, 'label': '120.14.4b1', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 0]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
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id: 5486503
{'center': '60.a1.a1', 'center_index': 60, 'center_order': 2, 'counter': 21, 'cyclotomic_n': 5, 'dim': 4, 'faithful': True, 'field': [-1, -1, 1], 'group': '120.14', 'group_counter': 14, 'group_order': 120, 'image': None, 'image_isoclass': '120.14', 'image_order': 120, 'indicator': -1, 'kernel': '120.a1.a1', 'kernel_order': 1, 'label': '120.14.4b2', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 0]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 61328566
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 120, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '120.14.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.14', 'subgroup_hash': 14, 'subgroup_order': 120, 'subgroup_tex': 'C_{15}:Q_8', 'supersolvable': True, 'sylow': 0}
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id: 61328577
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 60, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.14.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
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id: 61328583
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 60, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.14.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.2', 'subgroup_hash': 2, 'subgroup_order': 60, 'subgroup_tex': 'C_5:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 61328584
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 60, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.14.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.3', 'subgroup_hash': 3, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
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id: 61328585
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '120.14.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.4', 'subgroup_hash': 4, 'subgroup_order': 40, 'subgroup_tex': 'C_5:Q_8', 'supersolvable': True, 'sylow': 0}
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id: 61328586
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 30, 'counter': 6, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.14.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
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id: 61328587
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '120.14.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
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id: 61328588
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 20, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.14.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
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id: 61328589
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 10, 'counter': 9, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.14.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
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id: 61328567
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 10, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '120.14.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
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id: 61328568
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': True, 'core_order': 15, 'counter': 11, 'cyclic': True, 'direct': False, 'hall': 15, 'label': '120.14.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
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id: 61328569
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 12, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.14.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 61328570
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 13, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.14.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 61328571
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '120.14.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
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id: 61328572
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 10, 'counter': 15, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.14.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
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id: 61328573
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '120.14.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 2}
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id: 61328574
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 6, 'counter': 17, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.14.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 61328575
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 5, 'counter': 18, 'cyclic': True, 'direct': False, 'hall': 5, 'label': '120.14.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': True, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
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id: 61328576
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.14.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 61328578
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 20, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.14.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 61328579
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 21, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.14.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 61328580
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 3, 'counter': 22, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '120.14.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5:Q_8', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
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id: 61328581
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 2, 'counter': 23, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.14.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.8', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_5', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 61328582
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.14', 'ambient_counter': 14, 'ambient_order': 120, 'ambient_tex': 'C_{15}:Q_8', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 1, 'counter': 24, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '120.14.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '120.14', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D2', 'C5'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
Hide schema
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id: 61328571
{'ambient': '120.14', 'aut_centralizer_order': 8, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '12.4', 'aut_weyl_index': 40, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.c1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4831, -1, 9539, -1, 1887, -1, 4474, -1], 'generators': [3, 12, 8], 'label': '120.14.10.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 61328569
{'ambient': '120.14', 'aut_centralizer_order': 40, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 40, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9529, 8081, 4645, 8081, 3218, 2333, 7143, 7667], 'generators': [1, 12, 8], 'label': '120.14.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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id: 61328566
{'ambient': '120.14', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.a1.a1', 'complements': ['120.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6595, 5001, 6224, 5001, 5213, 5000, 5228, 5000], 'generators': [1, 12, 8, 6, 24], 'label': '120.14.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 61328567
{'ambient': '120.14', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '40.12', 'aut_weyl_index': 12, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '30.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2638, -1, 6514, -1, 4548, -1, 1864, -1], 'generators': [3, 24, 12], 'label': '120.14.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 61328568
{'ambient': '120.14', 'aut_centralizer_order': 60, 'aut_label': '8.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 60, 'centralizer': '4.a1.a1', 'complements': ['15.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['24.a1.a1', '40.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [471, 5001, 461, 5001, 2090, 5000, 1907, 5000], 'generators': [8, 24], 'label': '120.14.8.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['24.a1.a1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '120.14', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 61328570
{'ambient': '120.14', 'aut_centralizer_order': 24, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '4.2', 'aut_weyl_index': 120, 'centralizer': '10.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.b1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6662, -1, 7355, -1, 5850, -1, 8448, -1], 'generators': [6, 8, 12], 'label': '120.14.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 61328572
{'ambient': '120.14', 'aut_centralizer_order': 120, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 120, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '60.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2005, 2954, 2290, 2954, 4490, 7023, 3183, 2977], 'generators': [12, 24], 'label': '120.14.12.a1.a1', 'mobius_quo': 1, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '60.8', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 61328573
{'ambient': '120.14', 'aut_centralizer_order': 8, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 120, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.c1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7469, -1, 7724, -1, 9610, -1, 9608, -1], 'generators': [1, 6], 'label': '120.14.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 61328574
{'ambient': '120.14', 'aut_centralizer_order': 240, 'aut_label': '20.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 240, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'contains': ['40.a1.a1', '60.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4454, 7138, 5013, 7138, 3247, 3161, 4445, 6839], 'generators': [12, 8], 'label': '120.14.20.a1.a1', 'mobius_quo': 1, 'mobius_sub': -10, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['40.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '60.8', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.1', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 61328575
{'ambient': '120.14', 'aut_centralizer_order': 120, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 120, 'centralizer': '2.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1'], 'contains': ['120.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [942, 2632, 1065, 2632, 4432, 6747, 3183, 3253], 'generators': [24], 'label': '120.14.24.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '120.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 61328576
{'ambient': '120.14', 'aut_centralizer_order': 80, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 240, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7954, -1, 4289, -1, 6905, -1, 6838, -1], 'generators': [1], 'label': '120.14.30.a1.a1', 'mobius_quo': None, 'mobius_sub': -5, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 61328577
{'ambient': '120.14', 'aut_centralizer_order': 10, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.35', 'aut_weyl_index': 10, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.b1.a1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7967, 8288, 2684, 8288, 2798, 1713, 2806, 8287], 'generators': [1, 12, 8, 24], 'label': '120.14.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 61328578
{'ambient': '120.14', 'aut_centralizer_order': 48, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '2.1', 'aut_weyl_index': 240, 'centralizer': '10.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6379, -1, 6448, -1, 8178, -1, 8158, -1], 'generators': [6], 'label': '120.14.30.b1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 61328579
{'ambient': '120.14', 'aut_centralizer_order': 16, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 240, 'centralizer': '30.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '10.c1.a1', '15.a1.a1'], 'contains': ['60.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3594, -1, 8382, -1, 5647, -1, 5489, -1], 'generators': [3], 'label': '120.14.30.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.c1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 61328580
{'ambient': '120.14', 'aut_centralizer_order': 240, 'aut_label': '40.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 240, 'centralizer': '2.b1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1'], 'contains': ['120.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1682, 7552, 2078, 7552, 3247, 3437, 4358, 6563], 'generators': [8], 'label': '120.14.40.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '120.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.1', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 61328581
{'ambient': '120.14', 'aut_centralizer_order': 480, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 480, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1', '30.b1.a1', '30.c1.a1'], 'contains': ['120.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4360, 5070, 4698, 5070, 5604, 5092, 5461, 4908], 'generators': [12], 'label': '120.14.60.a1.a1', 'mobius_quo': -1, 'mobius_sub': 30, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.a1.a1', '20.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '60.8', 'quotient_action_image': '1.1', 'quotient_action_kernel': '60.8', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 61328582
{'ambient': '120.14', 'aut_centralizer_order': None, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1'], 'contains': [], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1682, 5070, 2078, 5070, 4432, 5092, 4358, 4908], 'generators': [], 'label': '120.14.120.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '120.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 61328583
{'ambient': '120.14', 'aut_centralizer_order': 6, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '80.50', 'aut_weyl_index': 6, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '10.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5208, 1712, 4882, 1712, 5213, 8287, 5228, 1713], 'generators': [6, 12, 24, 8], 'label': '120.14.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 61328584
{'ambient': '120.14', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '240.195', 'aut_weyl_index': 2, 'centralizer': '60.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.c1.a1', '10.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3244, 5001, 7264, 5001, 730, 5000, 732, 5000], 'generators': [3, 8, 24, 12], 'label': '120.14.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '60.8'}
-
id: 61328585
{'ambient': '120.14', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '80.50', 'aut_weyl_index': 6, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '15.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7092, -1, 5763, -1, 8424, -1, 7114, -1], 'generators': [1, 12, 24, 6], 'label': '120.14.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 61328586
{'ambient': '120.14', 'aut_centralizer_order': 60, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 60, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3109, 5001, 1711, 5001, 586, 5000, 558, 5000], 'generators': [12, 24, 8], 'label': '120.14.4.a1.a1', 'mobius_quo': -1, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '60.8', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 61328587
{'ambient': '120.14', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '24.14', 'aut_weyl_index': 20, 'centralizer': '60.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1', '15.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8936, -1, 8368, -1, 7093, -1, 8448, -1], 'generators': [1, 6, 12, 8], 'label': '120.14.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
-
id: 61328588
{'ambient': '120.14', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '40.12', 'aut_weyl_index': 12, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '30.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5343, 1919, 4803, 1919, 8424, 7667, 5809, 2310], 'generators': [6, 24, 12], 'label': '120.14.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
-
id: 61328589
{'ambient': '120.14', 'aut_centralizer_order': 20, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.2', 'aut_weyl_index': 60, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '30.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7066, -1, 3118, -1, 7122, -1, 3169, -1], 'generators': [1, 12, 24], 'label': '120.14.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '60.8', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
